Refining and relating fundamentals of functional theory

Abstract

To advance the foundation of one-particle reduced density matrix functional theory (1RDMFT) we refine and relate some of its fundamental features and underlying concepts. We define by concise means the scope of a 1RDMFT, identify its possible natural variables and explain how symmetries could be exploited. In particular, for systems with time-reversal symmetry, we explain why there exist six equivalent universal functionals, prove concise relations among them and conclude that the important notion of $v$-representability is relative to the scope and choice of variable. All these fundamental concepts are then comprehensively discussed and illustrated for the Hubbard dimer and its generalization to arbitrary pair interactions $W$. For this, we derive by analytical means the pure and ensemble functionals with respect to both the real- and complex-valued Hilbert space. The comparison of various functionals allows us to solve the underlying $v$-representability problems analytically and the dependence of its solution on the pair interaction is demonstrated. Intriguingly, the gradient of each universal functional is found to always diverge repulsively on the boundary of the domain. In that sense, this key finding emphasizes the universal character of the fermionic exchange force, recently discovered and proven in the context of translationally-invariant one-band lattice models.

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• Neutral electronic excitations and derivative discontinuities: An extended $N$-centered ensemble density functional theory perspective
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• Softmax parameterization of the occupation numbers for natural orbital functionals based on electron pairing approaches
• Extracting Many-Body Quantum Resources within One-Body Reduced Density Matrix Functional Theory
• Orbital-Free Quasi-Density Functional Theory
• A toolbox of spin-adapted generalized Pauli constraints
• Time-Reversal Symmetry in RDMFT and pCCD with Complex-Valued Orbitals
• Capturing electron correlation at mean-field cost: Assessment of i-DMFT and the underlying correlation conjecture
• Solving one-body ensemble N-representability problems with spin
• Refining ensemble $N$-representability of one-body density matrices from partial information
• Spin adaptation of the cumulant expansions of reduced density matrices